Abstract
We examine the evolution of highly eccentric, planet-crossing orbits in the planar restricted three-body problem (Sun, planet, comet), using a simple Keplerian map in which the comet energy changes instantaneously at perihelion by an amount depending only on the azimuthal angle between the planet and the comet at the time of perihelion passage. This approximate but very fast mapping allows us to explore the evolution of large ensembles of long-period comets. We compare our results on comet evolution with those given by the diffusion approximation and by direct integration of comet orbits. Our mapping suggests that at long times the number of surviving comets on highly eccentric, planet-crossing orbits may be determined by resonance sticking rather than a random walk.
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